Abstract: Using a simplified microstructural picture we show that interactions betweenthermosenstive microgel particles can be described by a polymer brush likecorona decorating the dense core. The softness of the potential is set by therelative thickness $L 0$ of the compliant corona with respect to the overallsize of the swollen particle $R$. The elastic modulus in quenched solid phasesderived from the potential is found in excellent agreement with diffusing wavespectroscopy DWS data and mechanical rheometry. Our model thus providesdesign rules for the microgel architecture and opens a route to tailorrheological properties of pasty materials.